Interaction response under area-preserving diffeomorphisms with time-dependent magnetic field

Determine how the interparticle interaction terms used to obtain fractional quantum Hall states transform under area-preserving diffeomorphisms when the external magnetic field B(t) is time-dependent, so that a consistent edge-mode theory can be formulated for fractional fillings in this setting.

Background

The paper develops a framework for quantum Hall systems subjected to time-dependent magnetic fields by extending the Ermakov method and constructing generalized Laughlin-type states. For edge dynamics, the integer case can be analyzed using area-preserving diffeomorphisms with a star-product formalism, but fractional states crucially depend on interparticle interactions.

The authors note a conceptual complication: when the magnetic field varies in time, the canonical structure preserved by edge excitations no longer directly corresponds to geometric area, and it is explicitly unclear how interaction terms behave under area-preserving diffeomorphisms in this time-dependent context. Resolving this is essential for extending their edge-mode analysis to fractional quantum Hall systems.